Your bank account pays a 5% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?
A) the periodic rate of interest is 5% and the effective rate of interest is also 5%.
B) the periodic rate of interest is 1.25% and the effective rate of interest is 2.5%.
C) the periodic rate of interest is 5% and the effective rate of interest is greater than 5%.
D) the periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%.
E) the periodic rate of interest is 2.5% and the effective rate of interest is 5%.

Question

Quizplus · Accepted Answer

The periodic rate of interest is the rate applied to determine the interest over one quarter which is one-fourth of a year. Therefore, periodic rate of interest is:

Periodic rate of interest = Nominal rate / number of periods per year

Periodic rate of interest = 5% / 4 quarters per year

Periodic rate of interest = 1.25%

To calculate the effective rate of interest, we use the formula:

Effective rate of interest = (1 + (nominal rate / number of periods per year))^number of periods per year - 1

Effective rate of interest = (1 + (5%/4))^4 - 1

Effective rate of interest = (1.0125)^4 - 1

Effective rate of interest = 5.12%

Therefore, the periodic rate of interest is 1.25% and the effective rate of interest is greater than 5%. Option D is the correct answer.

Your Bank Account Pays a 5% Nominal Rate of Interest